/**
* Returns the <a href="http://en.wikipedia.org/wiki/Rhumb_line">rhumb line</a> bearing from the
* current location to the GeoLocation passed in.
*
* @param location destination location
* @return the bearing in degrees
*/
public double getRhumbLineBearing(GeoLocation location) {
double dLon = Math.toRadians(location.getLongitude() - getLongitude());
double dPhi =
Math.log(
Math.tan(Math.toRadians(location.getLatitude()) / 2 + Math.PI / 4)
/ Math.tan(Math.toRadians(getLatitude()) / 2 + Math.PI / 4));
if (Math.abs(dLon) > Math.PI) dLon = dLon > 0 ? -(2 * Math.PI - dLon) : (2 * Math.PI + dLon);
return Math.toDegrees(Math.atan2(dLon, dPhi));
}
/**
* Returns the <a href="http://en.wikipedia.org/wiki/Rhumb_line">rhumb line</a> distance from the
* current location to the GeoLocation passed in.
*
* @param location the destination location
* @return the distance in Meters
*/
public double getRhumbLineDistance(GeoLocation location) {
double R = 6371; // earth's mean radius in km
double dLat = Math.toRadians(location.getLatitude() - getLatitude());
double dLon = Math.toRadians(Math.abs(location.getLongitude() - getLongitude()));
double dPhi =
Math.log(
Math.tan(Math.toRadians(location.getLongitude()) / 2 + Math.PI / 4)
/ Math.tan(Math.toRadians(getLatitude()) / 2 + Math.PI / 4));
double q = (Math.abs(dLat) > 1e-10) ? dLat / dPhi : Math.cos(Math.toRadians(getLatitude()));
// if dLon over 180° take shorter rhumb across 180° meridian:
if (dLon > Math.PI) dLon = 2 * Math.PI - dLon;
double d = Math.sqrt(dLat * dLat + q * q * dLon * dLon);
return d * R;
}
/**
* Calculate <a href="http://en.wikipedia.org/wiki/Great-circle_distance">geodesic distance</a> in
* Meters between this Object and a second Object passed to this method using <a
* href="http://en.wikipedia.org/wiki/Thaddeus_Vincenty">Thaddeus Vincenty's</a> inverse formula
* See T Vincenty, "<a href="http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf">Direct and Inverse
* Solutions of Geodesics on the Ellipsoid with application of nested equations</a>", Survey
* Review, vol XXII no 176, 1975
*
* @param location the destination location
* @param formula This formula calculates initial bearing ({@link #INITIAL_BEARING}), final
* bearing ( {@link #FINAL_BEARING}) and distance ({@link #DISTANCE}).
* @return geodesic distance in Meters
*/
private double vincentyFormula(GeoLocation location, int formula) {
double a = 6378137;
double b = 6356752.3142;
double f = 1 / 298.257223563; // WGS-84 ellipsiod
double L = Math.toRadians(location.getLongitude() - getLongitude());
double U1 = Math.atan((1 - f) * Math.tan(Math.toRadians(getLatitude())));
double U2 = Math.atan((1 - f) * Math.tan(Math.toRadians(location.getLatitude())));
double sinU1 = Math.sin(U1), cosU1 = Math.cos(U1);
double sinU2 = Math.sin(U2), cosU2 = Math.cos(U2);
double lambda = L;
double lambdaP = 2 * Math.PI;
double iterLimit = 20;
double sinLambda = 0;
double cosLambda = 0;
double sinSigma = 0;
double cosSigma = 0;
double sigma = 0;
double sinAlpha = 0;
double cosSqAlpha = 0;
double cos2SigmaM = 0;
double C;
while (Math.abs(lambda - lambdaP) > 1e-12 && --iterLimit > 0) {
sinLambda = Math.sin(lambda);
cosLambda = Math.cos(lambda);
sinSigma =
Math.sqrt(
(cosU2 * sinLambda) * (cosU2 * sinLambda)
+ (cosU1 * sinU2 - sinU1 * cosU2 * cosLambda)
* (cosU1 * sinU2 - sinU1 * cosU2 * cosLambda));
if (sinSigma == 0) return 0; // co-incident points
cosSigma = sinU1 * sinU2 + cosU1 * cosU2 * cosLambda;
sigma = Math.atan2(sinSigma, cosSigma);
sinAlpha = cosU1 * cosU2 * sinLambda / sinSigma;
cosSqAlpha = 1 - sinAlpha * sinAlpha;
cos2SigmaM = cosSigma - 2 * sinU1 * sinU2 / cosSqAlpha;
if (Double.isNaN(cos2SigmaM)) cos2SigmaM = 0; // equatorial line: cosSqAlpha=0 (§6)
C = f / 16 * cosSqAlpha * (4 + f * (4 - 3 * cosSqAlpha));
lambdaP = lambda;
lambda =
L
+ (1 - C)
* f
* sinAlpha
* (sigma
+ C
* sinSigma
* (cos2SigmaM + C * cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM)));
}
if (iterLimit == 0) return Double.NaN; // formula failed to converge
double uSq = cosSqAlpha * (a * a - b * b) / (b * b);
double A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)));
double B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)));
double deltaSigma =
B
* sinSigma
* (cos2SigmaM
+ B
/ 4
* (cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM)
- B
/ 6
* cos2SigmaM
* (-3 + 4 * sinSigma * sinSigma)
* (-3 + 4 * cos2SigmaM * cos2SigmaM)));
double distance = b * A * (sigma - deltaSigma);
// initial bearing
double fwdAz =
Math.toDegrees(Math.atan2(cosU2 * sinLambda, cosU1 * sinU2 - sinU1 * cosU2 * cosLambda));
// final bearing
double revAz =
Math.toDegrees(Math.atan2(cosU1 * sinLambda, -sinU1 * cosU2 + cosU1 * sinU2 * cosLambda));
if (formula == DISTANCE) {
return distance;
} else if (formula == INITIAL_BEARING) {
return fwdAz;
} else if (formula == FINAL_BEARING) {
return revAz;
} else { // should never happpen
return Double.NaN;
}
}